2017/11/02 by Maeda, Masaya, Sasaki, Hironobu, Segawa, Etsuo +2
#35Q55(Secondary) #81Q05(Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1711.00620
We study large time behavior of quantum walks (QW) with self-dependent coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate of (linear) QW such as Strichartz estimate. Such argument is standard in the study of nonlinear Schrödinger equations but it seems to be the first time to be applied to QW. We also numerically study the dynamics of QW and observe soliton like solutions.